Neutrino production coherence and oscillation experiments

TL;DR

This paper investigates the coherence conditions in neutrino production, compares different calculation methods, and analyzes how finite pion wave packet widths affect neutrino oscillation probabilities.

Contribution

It demonstrates the equivalence of two approaches to neutrino oscillation probability calculation under ideal conditions and explores decoherence effects due to finite pion wave packet widths.

Findings

The two calculation methods coincide for pointlike parent pions and perfect localization.

Finite pion wave packet width introduces corrections to the oscillation probability.

The correction magnitude depends on wave packet width, velocities, and oscillation length.

Abstract

Neutrino oscillations are only observable when the neutrino production, propagation and detection coherence conditions are satisfied. In this paper we consider in detail neutrino production coherence, taking \pi\to \mu \nu \ decay as an example. We compare the oscillation probabilities obtained in two different ways: (1) coherent summation of the amplitudes of neutrino production at different points along the trajectory of the parent pion; (2) averaging of the standard oscillation probability over the neutrino production coordinate in the source. We demonstrate that the results of these two different approaches exactly coincide, provided that the parent pion is considered as pointlike and the detection process is perfectly localized. In this case the standard averaging of the oscillation probability over the finite spatial extensions of the neutrino source (and detector) properly takes possible decoherence effects into account. We analyze the reason for this equivalence of the two approaches and demonstrate that for pion wave packets of finite width \sigma_{x\pi} the equivalence is broken. The leading order correction to the oscillation probability due to \sigma_{x\pi}\ne 0 is shown to be \sim [v_g/(v_g-v_\pi)]\sigma_{x\pi}/l_{osc}, where v_g and v_\pi \ are the group velocities of the neutrino and pion wave packets, and l_{osc} is the neutrino oscillation length.